The probability for the mean field in (REF ) is designed for a grid with a fixed neighbourhood size \(|\Gamma |\) . In the context of psychology and psychopathology, it is hard to come up with a graph representing the interactions between variables, that would take the form of a grid. We therefore also looked at the mean field model for a random graph and a small-world graph. A random graph \(G_{\rm rg}(n,p(e))\)  is a graph structure with \(n\)  nodes and a (constant) probability \(p(e)\)  for an edge to be present in the graph [1]}, [2]}. In the mean field model of a random graph, the neighbourhood size \(|\Gamma |\)  is a random variable that is maximally \(n-1\) . Each node has a binomial number of neighbours with expected number of neighbours \(p(e)(n-1)\) . We extend the idea used for the grid, where we marginalise over all possible configurations of number of active nodes for each neighbourhood of size \(n-1\)  for the random graph. One can approximate this probability accurately with a small modification of the probability used for a grid [3]}. The difference with the probability on the grid is in the size of the neighbourhood (see Figure REF , left and middle panel), where in the grid the neighbourhood size is fixed to \(|\Gamma |\) . In the mean field model for the random graph, we fix this to the expected number of neighbours \(p(e)(n-1)\) . Let \(\nu =\lfloor p(e)(n-1)\rfloor \)  be the integer part of the expected number of neighbours. For the random graph \(G_{\rm rg}\)  the neighbourhood size is no longer \(|\Gamma |\)  (like it is for the grid), but \(\nu \) . The probability in a random graph for a node to become active given the graph's density at time point \(t\)  (\(\rho _t\) ) and the edge probability then becomes [3]}:
\(\rho _{t+1}^{\rm rg} = \sum ^{\nu }_{r=0} \mathbb {P}(X_{i, t+1} = 1 \mid r){\nu \atopwithdelims ()r}\rho _t^r(1-\rho _t)^{\nu -r}\) 
